Description of problem:

When setting display_fqdn_for_hosts is disabled, for searching we use FQDN on all hosts page, as well on the Facts details page, but on REX job run page we use short-names for searching when setting is disabled, so there's an inconsistency here for searching, which we discussed in https://issues.redhat.com/browse/SAT-21371

How reproducible:

Always

Is this issue a regression from an earlier version:

No

Steps to Reproduce:

1.  Setup Satellite stream, register any hosts to it and disable setting display_fqdn_for_hosts

2. Navigate to Hosts -> All hosts -> Use search bar and type "name  = "

3. Navigate to Monitor -> Facts -> Use search bar and type "host  = "

4. Navigate to Monitor -> Audits -> Use search bar and type "host  = "

5. Navigate to Monitor -> Jobs -> Use search bar and type "host  = "

Actual behavior:
FQDN are used on all hosts page, on the Facts details page, but on REX job run page we use short-names for searching 

Expected behavior:
Use shortnames everywhere in search bar when setting is disabled, and when enabled use FQDNs to keep naming consistent everywhere.

Business Impact / Additional info:

Discussion: https://redhat-internal.slack.com/archives/C04LM3N1J5C/p1717511176160749